We present a detailed study of the static spherically symmetric solutions in de Rham–Gabadadze–Tolley (dRGT) theory. Since the diffeomorphism invariance can be restored by introducing the Stückelberg fields ${\varphi }^a$, there is new invariant $I^{ab}=g^{\mu \nu }{\partial }_{\mu }{\varphi }^a{\partial }_{\nu }{\varphi }^b$ in the massive gravity, which adds to the ones usually encountered in general relativity (GR). In the unitary gauge ${\varphi }^a=x^{\mu }{\delta }_{\mu }^a$, any inverse metric $g^{\mu \nu }$ that has divergence including the coordinate singularity in GR would exhibit a singularity in the invariant $I^{ab}$. Therefore, there is no conventional Schwarzschild metric if we choose unitary gauge. In this paper, we obtain a self-consistent static spherically symmetric ansatz in the nonunitary gauge. Under this ansatz, we find that there are seven solutions including the Schwarzschild solution, Reissner-Nordström solution and five other solutions. These solutions may possess an event horizon depending upon the physical parameters (Schwarzschild radius $r_s$, scalar charge $S$ and/or electric charge $Q$). If these solutions possess an event horizon, we show that the singularity of $I^{ab}$ is absent at the horizon. Therefore, these solutions may become candidates for black holes in dRGT.

Large-scale structure surveys in the coming years will measure the redshift-space power spectrum to unprecedented accuracy, allowing for powerful new tests of the $\mathrm{\Lambda }$ cold dark matter ($\mathrm{\Lambda }\mathrm{CDM}$) picture as well as measurements of particle physics parameters such as the neutrino masses. We extend the time-renormalization-group (RG) perturbative framework to redshift space, computing the power spectrum $P_s(k,\mu )$ in massive neutrino cosmologies with time-dependent dark energy equations of state $w(z)$. Time-RG is uniquely capable of incorporating scale-dependent growth into the $P_s(k,\mu )$ computation, which is important for massive neutrinos as well as modified gravity models. Although changes to $w(z)$ and the neutrino mass fraction both affect the late-time scale dependence of the nonlinear power spectrum, we find that the two effects depend differently on the line-of-sight angle $\mu$. Finally, we use the hacc N-body code to quantify errors in the perturbative calculations. For a $\mathrm{\Lambda }\mathrm{CDM}$ model at redshift $z=1$, our procedure predicts the monopole (quadrupole) to 1% accuracy up to a wave number $0.19h/\mathrm{Mpc}$ ($0.28h/\mathrm{Mpc}$), compared to $0.08h/\mathrm{Mpc}$ ($0.07h/\mathrm{Mpc}$) for the Kaiser approximation and $0.19h/\mathrm{Mpc}$ ($0.16h/\mathrm{Mpc}$) for the current state-of-the-art perturbation scheme. Our calculation agrees with the simulated redshift-space power spectrum even for neutrino masses above the current bound, and for rapidly evolving dark energy equations of state, $|dw/dz|\sim 1$. Along with this article, we make our redshift-space time-RG implementation publicly available as the code redtime.

Recently, we have shown that the propagation speed $c_T$ of the primordial gravitational waves (GWs) might be nontrivially varying during inflation, which could induce local oscillations in the power spectrum of primordial GWs. In this paper, we numerically confirm that, although with a disformal redefinition of the metric the nontrivial $c_T$ may be set as unity, the power spectrum in the frame with $c_T=1$ is completely the same as that in the original disformal frame, i.e., the oscillating shape in the power spectrum is still reserved, since here the effect of $c_T$ is actually encoded in the nontrivially varying Hubble parameter. In addition, we also clarify how to obtain a blue-tilted GWs spectrum by imposing a rapidly decreasing $c_T$ during inflation.

We propose a new framework of low-scale gauge-mediated supersymmetry (SUSY) breaking with a gravitino mass of $\mathcal{\text{O}}(100)\mathrm{TeV}$. The usual 4D gauge mediation models predict a light gravitino and suffer from cosmological problems. In our framework, a heavy gravitino in gauge mediation is realized with a flat extra dimension, whose compactification scale is around the grand unified theory scale. Superparticle masses of the visible sector from gravity/anomaly mediation are suppressed, and they are purely generated by the usual gauge mediation on the visible brane. Importantly, the Higgs $B_{\mu }$-term vanishes at the leading order, which enables us to obtain the suitable $\mu \text{−}{B}_{\mu }$ relation for the electroweak symmetry breaking. We discuss such models considering two possibilities of the SUSY breaking source: (1) Scherk-Schwarz SUSY breaking which we call Scherk-Schwarz gauge mediation and (2) gravitational SUSY breaking localized on a hidden brane. In case (2), the cosmological moduli problem may be relaxed as well.

We present a general formalism for computing the matrix-element squared for the emission of soft energy-ordered gluons beyond two loops in QCD perturbation theory at finite $N_c$. Our formalism is valid in the eikonal approximation. A Mathematica program has been developed for the automated calculation of all real/virtual eikonal squared amplitudes needed at a given loop order. For the purpose of illustration, we show the explicit forms of the eikonal squared amplitudes up to the fifth-loop order. In the large-$N_c$ limit, our results coincide with those previously reported in literature.

In this paper we extend the color dipole formalism to the study of exclusive processes associated with a leading neutron in $ep$ collisions at high energies. The exclusive $\rho$, $\varphi$ and $J/\mathrm{\Psi }$ production, as well as the deeply virtual Compton scattering, are analyzed assuming a diffractive interaction between the color dipole and the pion emitted by the incident proton. We compare our predictions with the HERA data on $\rho$ production and estimate the magnitude of the absorption corrections. We show that the color dipole formalism is able to describe the current data. Finally, we present our estimate for the exclusive cross sections which can be studied at HERA and in future electron-proton colliders.

We demonstrate the usefulness of flavor neutrino masses expressed in terms of $M_{ee}$, $M_{e\mu }$ and $M_{e\tau }$. The analytical expressions for the flavor neutrino masses, mass eigenstates and physical $CP$-violating Majorana phases for texture two zeros are obtained exactly.

The creation of electron-positron pairs by the strong-field Breit-Wheeler process in intense short laser pulses is investigated in the framework of laser-dressed quantum electrodynamics. Regarding laser field parameters in the multiphoton regime, special attention is brought to the energy spectrum of the created particles, which can be reproduced and explained by means of an intuitive model. The model is based on the probabilities of multiphoton events driven by the spectral components of the laser pulse. It allows us, in particular, to identify interferences between different pair production channels which exhibit a characteristic dependence on the laser carrier-envelope phase.

We develop the $1/N$ expansion for stable string bit models, focusing on a model with bit creation operators carrying only transverse spinor indices $a=1,\dots ,s$. At leading order ($N=\infty$), this model produces a (discretized) light cone string with a “transverse space” of $s$ Grassmann worldsheet fields. Higher orders in the $1/N$ expansion are shown to be determined by the overlap of a single large closed chain (discretized string) with two smaller closed chains. In the models studied here, the overlap is not accompanied with operator insertions at the break/join point. Then, the requirement that the discretized overlap has a smooth continuum limit leads to the critical Grassmann “dimension” of $s=24$. This “protostring,” a Grassmann analog of the bosonic string, is unusual, because it has no large transverse dimensions. It is a string moving in one space dimension, and there are neither tachyons nor massless particles. The protostring, derived from our pure spinor string bit model, has 24 Grassmann dimensions, 16 of which could be bosonized to form 8 compactified bosonic dimensions, leaving 8 Grassmann dimensions—the worldsheet content of the superstring. If the transverse space of the protostring could be “decompactified,” string bit models might provide an appealing and solid foundation for superstring theory.

Nambu–Jona-Lasinio (NJL) interactions are introduced into the D3/probe D7 system using Witten’s double trace operator prescription which includes the operator as a classical term in the effective potential. In the supersymmetric system the interactions do not induce chiral symmetry breaking, which we attribute to the flat effective potential with quark mass in the supersymmetric theory. If additional supersymmetry breaking is introduced, then standard NJL behavior is realized. In examples where chiral symmetry breaking is not preferred, such as with a $B$ field plus an IR cutoff, chiral condensation is triggered by the NJL interaction at a second-order transition after a finite critical coupling. If the model already contains chiral symmetry breaking, for example in the $B$ field case with no IR cutoff, then the NJL interaction enhances the quark mass at all values of the NJL coupling. We also consider the system at finite temperature: the temperature discourages condensation, but when combined with a magnetic field, we find regions of parameter space where the NJL interaction triggers a first-order chiral transition above a critical coupling.

We study the effects of D-brane instantons wrapping rigid cycles on the ${\mathbb{Z}}_2\times {\mathbb{Z}}_2^{\prime }$ toroidal orbifold. We compute Majorana masses induced by rigid D-brane instantons and realize bimaximal mixing matrices in certain models. We can also derive more generic mass matrices in other models. The bimaximal mixing Majorana mass matrix provides a possibility for explaining observed mixing angles. We also compute the $\mu$-term matrix among more than one pair of Higgs fields induced by rigid D-brane instantons.

In this work we find the general static vacuum solution of three-dimensional gravity with negative cosmological constant. Even though all solutions are locally diffeomorphic to pure ${\mathrm{AdS}}_3$, solutions that differ globally from the latter space exist. New solutions with black holes on the ${\mathrm{AdS}}_3$ boundary are found in both global and Poincare coordinates. In the Poincare coordinates such solutions are known as black funnels and black droplets. The black funnel provided by our general static metric is dual to the Hartle-Hawking state in the $1+1$ boundary theory.

We discuss a Coulomb gas realization of $n$-point correlation functions in the $SL(2,\mathbb{R})$ Wess-Zumino-Witten (WZW) model that is suitable to compute scattering amplitudes of winding strings in three-dimensional anti–de Sitter space at tree level and one loop. This is a refined version of previously proposed free-field realizations that, among other features, make the $H_3^{+}$ WZW-Liouville correspondence manifest.

This paper investigates the decays from heavy Higgsino-like weak doublets into $Z$, $h$ bosons and missing particles. When pair-produced at the LHC, the subsequent $Z$, $h\to \ell \ell$, $b\overline{b}$ decays in the doublet decay cascade can yield $4\ell$, $2\ell 2b$ and $4b+{\cancel{E}}_{\mathrm{T}}+j(\mathrm{s})$ final states. Mutual observation of any two of these channels would provide information on the associated doublets’ decay branching fractions into a $Z$ or $h$, thereby probing the Goldstone equivalence relation, shedding additional light on the Higgs sector of beyond the Standard Model theories and facilitating the discrimination of various contending models, in turn. We compare the $Z/h$ decay ratio expected in the minimal supersymmetric model, the next-to-minimal supersymmetric model (NMSSM)and a minimal singlet-doublet dark matter model. Additionally, we conduct a full Monte Carlo analysis of the prospects for detecting the targeted final states during 14 TeV running of the LHC in the context of a representative NMSSM benchmark model.

We investigate the mass spectra of open heavy flavor mesons in an external constant magnetic field within QCD sum rules. Spectral Ansätze on the phenomenological side are proposed in order to properly take into account mixing effects between the pseudoscalar and vector channels, and the Landau levels of charged mesons. The operator product expansion is implemented up to dimension-5 operators. As a result, we find for neutral $D$ mesons a significant positive mass shift that goes beyond simple mixing effects. In contrast, charged $D$ mesons are further subject to Landau level effects, which together with the mixing effects almost completely saturate the mass shifts obtained in our sum rule analysis.

We compute Green’s functions with a bilinear quark operator inserted at nonzero momentum for a generalized momentum configuration to two loops. These are required to assist lattice gauge theory measurements of the same quantity in matching to the high energy behavior. The flavor nonsinglet operators considered are the scalar, vector and tensor currents as well as the second moment of the twist-2 Wilson operator used in deep inelastic scattering for the measurement of nucleon structure functions.

The nonlinear O(3) $\sigma$ model in ($2+1$) dimensions with an additional potential term admits solutions called Q-lumps, having both topological and Noether charges. We consider in $3+1$-dimensional spacetime the theory with Q-lumps on a domain wall in the presence of spin-orbit interaction in the bulk and find interaction effects for a two-particle solution through perturbation theory and adiabatic approximation.

We study charged, static, topological black holes in pure Gauss-Bonnet gravity in asymptotically AdS space. As in general relativity, the theory possesses a unique nondegenerate AdS vacuum. It also admits charged black hole solutions which asymptotically behave as the Reissner-Nordström AdS black hole. We discuss black hole thermodynamics of these black holes. Then we study phase transitions in a dual quantum field theory in four dimensions, with the Stückelberg scalar field as an order parameter. We find in the probe limit that the black hole can develop hair below some critical temperature, which suggests a phase transition. Depending on the scalar coupling constants, the phase transition can be first or second order. Analysis of the free energy reveals that, comparing the two solutions, the hairy state is energetically favorable, thus a phase transition will occur in a dual field theory.

This paper investigates the nonlinear structure formation in a spherical top-hat collapse model based on the pseudo-Newtonian approximation. The system is composed of warm dark matter and dark energy and the dynamical properties of the collapsing region are analyzed for various parametrizations of the dark matter equation of state which are in agreement with current observations. Concerning dark energy, observational constraints of the Chevallier-Polarski-Linder model and the Jassal-Bagla-Padmanabhan equation of state have been considered. During the collapse, the positive dark matter pressure leads to an increase of growth for dark matter and dark energy perturbations and an accelerated expansion for the spherical region. Hence, in the warm dark matter hypothesis, the structure formation is accelerated and the inconsistencies of the $\mathrm{\Lambda }\mathrm{CDM}$ model at the galactic scales could be solved. The results obtained are applicable only to adiabatic warm dark matter physical models which are compatible with the pseudo-Newtonian approach.

We investigate the preinflationary dynamics of inflation with the Starobinsky potential, favored by recent data from the Planck mission, using techniques developed to study cosmological perturbations on quantum spacetimes in the framework of loop quantum cosmology. We find that for a large part of the initial data, inflation compatible with observations occurs. There exists a subset of this initial data that leads to quantum gravity signatures that are potentially observable. Interestingly, despite the different inflationary dynamics, these quantum gravity corrections to the power spectra are similar to those obtained for inflation with a quadratic potential, including suppression of power at large scales. Furthermore, for superhorizon modes the tensor modes show deviations from the standard inflationary paradigm that are unique to the Starobinsky potential and could be important for non-Gaussian modulation and tensor fossils.